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A340539 a(n) is the least prime that is the concatenation of two n-digit primes, and such that the concatenation of the same primes in the other order is also prime or 0 if no such prime exists.

%I A340539 #16 Jan 13 2021 10:40:50
%S A340539 37,1123,101107,10091789,1000710709,100003100363,10000031000303,
%T A340539 1000001910002521,100000007100010321,10000000071000000349,
%U A340539 1000000001910000000799,100000000003100000009939,10000000000391000000012387,1000000000003710000000034573,100000000000031100000000014113
%N A340539 a(n) is the least prime that is the concatenation of two n-digit primes, and such that the concatenation of the same primes in the other order is also prime or 0 if no such prime exists.
%C A340539 Conjecture: a(n) > 0 and for n > 1 the first n digits of a(n) = A003617(n). - _Chai Wah Wu_, Jan 13 2021
%H A340539 Robert Israel, <a href="/A340539/b340539.txt">Table of n, a(n) for n = 1..171</a>
%e A340539 For n=4, 1009, 1789, 10091789 and 17891009 are all prime.
%p A340539 f:= proc(d) local P,a,b;
%p A340539   a:= prevprime(10^(d-1));
%p A340539   do
%p A340539     a:= nextprime(a);
%p A340539     if a > 10^d then return FAIL fi;
%p A340539     b:= prevprime(10^(d-1));
%p A340539     do
%p A340539       b:= nextprime(b);
%p A340539       if b > 10^d then break fi;
%p A340539       if isprime(10^d*a+b) and isprime(10^d*b+a) then return 10^d*a+b fi;
%p A340539   od od:
%p A340539   FAIL
%p A340539 end proc:
%p A340539 f(1):= 37:
%p A340539 map(f, [$1..20]);
%Y A340539 Cf. A003617, A340487.
%K A340539 nonn,base
%O A340539 1,1
%A A340539 _J. M. Bergot_ and _Robert Israel_, Jan 10 2021